Abstract
The author defines a new construction of free product in the variety of profinite groups of the family of groups in , continuously indexed by points of the profinite space . In the case where is closed relative to extensions with Abelian kernels, a number of assertions about the homology groups of are obtained. Using homological methods, a theorem of Kurosh type on decomposition of an arbitrary pro--subgroup in into a free pro--product is proved, under a certain separability condition on . Bibliography: 19 titles.
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